In this paper, the problem of output synchronization is investigated for the heterogeneous network with an uncertain leader. It is assumed that parameter perturbations influence the nonidentical linear agents, whose outputs are controlled to track the output of an uncertain leader. Based on the hierarchical structure of the communication graph, a novel control scheme is proposed to guarantee the output synchronization. As there exist parameter uncertainties in the models of the agents, the internal model principle is used to gain robustness versus plant parameter uncertainties. Furthermore, as the precise model of the leader is also not available, the adaptive control principle is adopted to tune the parameters in the local controllers. The developed new technique is able to simultaneously handle uncertainties in the follower parameters as well as the leader parameters. The agents in the upper layers will be treated as the exosystems of the agents in the lower layers. The local controllers are constructed in a sequential order. It is shown that the output synchronization can be achieved globally asymptotically and locally exponentially. Finally, a simulation example is given to illustrate the effectiveness and potential of the theoretic results obtained.